Definition of entropy change:

$$\mathrm{\Delta }S=\int \frac{d{Q}_{rev}}{T}$$

only true for reversible heat transfer $(Q)$and must use absolute temperature, $T$

Entropy change for a phase change:

$$\mathrm{\Delta }S=\frac{\mathrm{\Delta }H}{T}$$

where $\mathrm{\Delta }H$ is the enthalpy change for the phase change and $T$ is the absolute temperature at which the phase change take place.

Entropy change (per mole of mixture) of mixing ideal gases at constant temperature and constant pressure:

$$\mathrm{\Delta }S=-R\sum y_{i}ln{y}_i$$

where $R$ is the ideal gas constant, and $y_i$ is the mole fraction of component $i$ in the gas phase.

Entropy change per mole for an ideal gas where initial state s $P_1,V_1,T_1$ and the final state $P_2,V_2,T_2$:

$$\mathrm{\Delta }S=C_{P}ln\left(\frac{T_2}{T_1}\right)–Rln\left(\frac{P_2}{P_1}\right)$$

$$\mathrm{\Delta }S=C_{V}ln\left(\frac{T_2}{T_1}\right)+Rln\left(\frac{V_2}{V_1}\right)$$

where the heat capacities $(C_P,C_V)$ are constant.

Entropy change for liquids or solids when temperature increases from $T_1$ to $T_2$ :

$$\mathrm{\Delta }S=C_{P}ln\left(\frac{T_2}{T_1}\right)$$

where $C_P$ is the heat capacity, which is assumed constant for a liquid or solid. Absolute temperature must be used in this equation. At most pressures, the entropy of liquids or solids does not change significantly when the pressure changes.